Problem: The geometric sequence $(a_i)$ is defined by the formula: $a_i = -2 \left(-4\right)^{i - 1}$ What is $a_{3}$, the third term in the sequence?
Explanation: From the given formula, we can see that the first term of the sequence is $-2$ and the common ratio is $-4$ To find $a_{3}$ , we can simply substitute $i = 3$ into the given formula. Therefore, the third term is equal to $a_{3} = -2 \left(-4\right)^{3 - 1} = -32$.